The volume of one or more compounds (e.g., quartz and calcite) in a rock formation may be calculated if the chemical and/or mineral components (e.g., elements) in the rock formation are known. The equations for this relationship are:Ysilicon=(0)(Vcalcite)+(Psil)(Vquartz)Ycalcium=(Pcal)(Vcalicite)+(0)(Vquartz)where represents the yield of the chemical component silicon, Ycalcium represents the yield of the chemical component calcium, Psil represents the proportion of silicon in quartz (SiO2) mineral, Pcal represents the proportion of calcium in calcite (CaCO3) mineral, Vcalcite is the volume of calcite, and Vquartz is the volume of quartz.
The current implementation of geochemical log processing provides relative yields of the chemical components defined as the ratio of the yields of the chemical components. For example, the equation may be
      RY    CA    =            Y      calcium                      Y        silicon            +              Y        calcium            +      …      +              Y        background            where RYCA represents the relative yield of calcium.
The algebraic simplification of this method may lead to inconsistency when fluids or other chemical components (e.g., elements) that are not described by the relative yields are introduced in the inversion system. Those fluids and components may then be overestimated. Additionally, the weighted vector mix of the relative yields in the denominator may lead to confusion when analyzing the results of reconstructed yields from the inversion.